Loans Data Sheet - Nuffield Foundation · Web viewgraph paper Excel spreadsheet Mammals.xls...
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Photo-copiable A Resource for Free-standing Mathematics Units Mammals Mammals The data given below was compiled by researchers Allison, Truett and Cicchetti and used in their article ‘Sleep in Mammals:Ecological and Constitutional Correlates’ (1976). The table below gives typical values of the following variables for small mammals: body mass in kilograms brain mass in grams sleep in hours per day – this includes both paradoxical (dreaming) sleep and slow wave (non-dreaming) sleep maximum life span in years gestation time in days i.e. the period the young is carried in the womb before birth overall danger index – a combined index reflecting levels of predation danger (likelihood of being preyed upon) and sleep exposure 1 = least danger from other animals 5 = most danger from other animals An entry of ‘NA’ means that the information is not available. University of Manchester 1 Mathematics for all post-16 – A project funded by the Nuffield Foundation Data Sheet 1
Transcript of Loans Data Sheet - Nuffield Foundation · Web viewgraph paper Excel spreadsheet Mammals.xls...
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A Resource for Free-standing Mathematics Units Mammals
Mammals
The data given below was compiled by researchers Allison, Truett and Cicchetti and used in their article ‘Sleep in Mammals:Ecological and Constitutional Correlates’ (1976).
The table below gives typical values of the following variables for small mammals: body mass in kilograms brain mass in grams sleep in hours per day – this includes both paradoxical (dreaming) sleep and slow
wave (non-dreaming) sleep maximum life span in years gestation time in days i.e. the period the young is carried in the womb before birth overall danger index – a combined index reflecting levels of predation danger
(likelihood of being preyed upon) and sleep exposure1 = least danger from other animals 5 = most danger from other animals
An entry of ‘NA’ means that the information is not available.
University of Manchester 1Mathematics for all post-16 – A project funded by the Nuffield Foundation
Data Sheet 1
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A Resource for Free-standing Mathematics Units Mammals
Mammals
The data given below was compiled by researchers Allison, Truett and Cicchetti and used in their article ‘Sleep in Mammals:Ecological and Constitutional Correlates’ (1976).
The table below gives typical values of the following variables for medium-sized mammals: body mass in kilograms brain mass in grams sleep in hours per day – this includes both paradoxical (dreaming) sleep and slow
wave (non-dreaming) sleep maximum life span in years gestation time in days i.e. the period the young is carried in the womb before birth overall danger index – a combined index reflecting levels of predation danger
(likelihood of being preyed upon) and sleep exposure1 = least danger from other animals 5 = most danger from other animals
An entry of ‘NA’ means that the information is not available.
University of Manchester 2Mathematics for all post-16 – A project funded by the Nuffield Foundation
Data Sheet 2
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A Resource for Free-standing Mathematics Units Mammals
Mammals
The data given below was compiled by researchers Allison, Truett and Cicchetti and used in their article ‘Sleep in Mammals:Ecological and Constitutional Correlates’ (1976).
The table below gives typical values of the following variables for large mammals: body mass in kilograms brain mass in grams sleep in hours per day – this includes both paradoxical (dreaming) sleep and slow
wave (non-dreaming) sleep maximum life span in years gestation time in days i.e. the period the young is carried in the womb before birth overall danger index – a combined index reflecting levels of predation danger
(likelihood of being preyed upon) and sleep exposure1 = least danger from other animals 5 = most danger from other animals
An entry of ‘NA’ means that the information is not available.
University of Manchester 3Mathematics for all post-16 – A project funded by the Nuffield Foundation
Data Sheet 3
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A Resource for Free-standing Mathematics Units Mammals
Mammals
The data provided includes the body mass, brain mass, sleep, maximum life span, gestation time and a danger index for a variety of mammals.
Choose a pair of variables which you think may be related.Investigate whether the data provides any evidence to support your theory.
Remember that you should: identify clearly the purpose of your investigation select and use appropriate statistical measures, diagrams and techniques.
To achieve a high mark you will need to show that you can work independently produce work which is clear, logical and well-structured check your work use appropriate, efficient and concise methods
University of Manchester 4Mathematics for all post-16 – A project funded by the Nuffield Foundation
Assignment
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A Resource for Free-standing Mathematics Units Mammals
use mathematics to correctly summarise your work and draw valid, relevant and accurate conclusions
critically consider how the data available has limited your work and what additional data would improve your study.
University of Manchester 5Mathematics for all post-16 – A project funded by the Nuffield Foundation
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A Resource for Free-standing Mathematics Units Mammals
Unit Advanced Level, Using and applying statistics
Skills which may be used in this assignment: drawing scatter diagrams finding lines of best fit calculating correlation coefficients
PreparationFor the assignment students will need: copies of one or more of the data sheets (pages 1 - 3) copy of the assignment (page 4) graph paper Excel spreadsheet Mammals.xls (optional)
Notes on the AssignmentThe multiple regression analysis carried out by Allison, Truett and Cicchetti is beyond the scope of this unit, but the data they compiled has been used as the basis of the assignment. You can opt to use either one, two or all three data sheets.The assignment is very open-ended allowing students to use a variety of approaches. Students are asked to investigate the relationship between a pair of variabes of their choice. There are obviously a large number of possibilities - in many of these there will be little evidence of correlation. It is important that students realise the importance of drawing a scatter diagram to give an indication of whether any relationship exists between two variables, rather than assuming that it does and relying solely on the calculation of correlation coefficients. They will need to decide what to do where no data is available and make decisions on how to deal with outliers (eg elephants and man in the large mammal data).Pages 6 - 11 give examples of the scatter diagrams, lines of best fit and correlation coefficients which might be produced by students investigating the relationship between brain mass and body mass. These have been done using the Excel spreadsheet, Mammals.xls. This spreadsheet is available for downloading so that students can be given the choice of working by hand or electronically.
AlternativesOne section of the data could be used to illustrate the methods associated with correlation , with students then using other sections for practice. The scatter diagrams could be copied onto OHP transparencies and used for class discussion. Important discussion points include: close grouping of small mammals when all data is used the problem of outliers values of correlation coefficients and the corresponding scatter diagrams the effect grouping data has on scatter diagrams, correlation coefficients and
equations of lines of best fit.
University of Manchester 6Mathematics for all post-16 – A project funded by the Nuffield Foundation
Teacher Notes
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A Resource for Free-standing Mathematics Units Mammals
Scatter Diagram of Brain Mass against Body MassSmall Mammals
Pearson’s product moment correlation coefficient 0.534
Line of Best Fit y = 6.77x + 1.45Mean values (0.299, 3.47) shown as
University of Manchester 7Mathematics for all post-16 – A project funded by the Nuffield Foundation
Body Mass (kg)
Bra
in M
ass (
g)
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A Resource for Free-standing Mathematics Units Mammals
Scatter Diagram of Brain Mass against Body MassMedium Mammals
Pearson’s product moment correlation coefficient 0.806
Line of Best Fit y = 16.1x –19.6
University of Manchester 8Mathematics for all post-16 – A project funded by the Nuffield Foundation
Body Mass (kg)
Bra
in M
ass (
g)
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A Resource for Free-standing Mathematics Units Mammals
Mean values (3.23, 32.5) shown as
University of Manchester 9Mathematics for all post-16 – A project funded by the Nuffield Foundation
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A Resource for Free-standing Mathematics Units Mammals
Scatter Diagram of Brain Mass against Body MassLarge Mammals
Pearson’s product moment correlation coefficient 0.930
Line of Best Fit y = 0.927x + 260Mean values (583, 800) shown as
University of Manchester 10Mathematics for all post-16 – A project funded by the Nuffield Foundation
Body Mass (kg)
Bra
in M
ass (
g)
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A Resource for Free-standing Mathematics Units Mammals
Scatter Diagram of Brain Mass against Body MassLarge Mammals without elephants and man
Pearson’s product moment correlation coefficient 0.831
Line of Best Fit y = 0.951x + 129Mean values (166, 287) shown as
University of Manchester 11Mathematics for all post-16 – A project funded by the Nuffield Foundation
Body Mass (kg)
Bra
in M
ass (
g)
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A Resource for Free-standing Mathematics Units Mammals
Scatter Diagram of Brain Mass against Body MassAll Mammals
Pearson’s product moment correlation coefficient 0.934
Line of Best Fit y = 0.967x + 91.0Mean values (199, 283) shown as
University of Manchester 12Mathematics for all post-16 – A project funded by the Nuffield Foundation
Body Mass (kg)
Bra
in M
ass (
g)
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A Resource for Free-standing Mathematics Units Mammals
Scatter Diagram of Brain Mass against Body MassAll Mammals without outliers (elephants)
Pearson’s product moment correlation coefficient 0.651
Line of Best Fit y = 1.24x + 56.0Mean values (52.1, 121) shown as
University of Manchester 13Mathematics for all post-16 – A project funded by the Nuffield Foundation
Body Mass (kg)
Bra
in M
ass (
g)
